It is very noticeable cycling in France that the drivers that cut you up are often the Brits - the French are very respectful of cyclists. Some of that is that they have a cycling culture so drivers are more likely to have cycled themselves, but a lot of it is the assumed liability law.
The CTC have a campaign called SMIDSY because so many drivers defense, after they have knocked over a cyclist, is "sorry mate I didn't see you".
Drivers who know they are going to have to prove they didn't do anything stupid are less likely to do something stupid.
And yes, there are many annoying and irresponsible cyclists around, but they are far less likely to kill or seriously injure people than drivers:
In 2012, 1 pedestrian was killed by a cyclist and 78 were seriously injured. 60% of pedestrians injured by cyclists were at fault, having stepped into the road without looking.
In the same year, 253 pedestrians were killed by drivers and 4,426 were seriously injured.
Also in the same year , 118 cyclists were killed by drivers. Deaths to cyclists are the only kind of traffic incident to be steadily rising.
There are definitely some dreadful cyclists out there, but we car drivers do have to recognise that we are driving a potentially dangerous weapon and we need to give cyclists room and respect on the roads. That's what this legislation would be aiming to promote. I'd be all for it.